Answer:
90°, 60°, and 30°
60°.
Step-by-step explanation:
The triangle ABC has side lengths √6, √2, and 2√2 units.
It is clear that the triangle ABC is right triangle because (2√2)² = (√6)² + (√2)² that means the side lengths satisfy the Pythagoras Theorem.
Now, if the angle between hypotenuse (2√2 units) and base (√2 units) is 
, then
Hence, = 60°
Therefore, the three angles of the triangle are 90°, 60°, and 30°.
Now, if the base of the triangle is 16 units, then other two side lengths will also change proportionally to remain the triangle a right triangle.
And in that case the base angle will remain 60°. (Answer)
Answer:
0.0433
Step-by-step explanation:
Since we have a fixed number of trials (N = 25) and the probability of getting heads is always p = 0.05, we are going to treat this as a binomial distribution.
Using a binomial probability calculator, we find that the probability of obtaining heads from 8 to 17 times is 0.9567 given that the con is fair. The probability of obtaining any other value given that the coin is fair is going to be:
1 - 0.9567 = 0.0433
Since we are going to conclude that the coin is baised if either x<8 or x>17, the probability of judging the coin to be baised when it is actually fair is 4.33%
We solve for the diameters of radius of the given circles by using the equation,
C = πD
or C = 2πr
where D and r are diameter and radius, respectively.
Solving,
C = 34.54 units
D = C/π = 34.54 units / 3.14 = 11 units
r = C / 2π = 34.54 units/2(3.14) = 5.5 units
C = 59.66 units
D = C/π = 59.66 units/3.14 = 19 units
r = D2 = 9.5 units
C = 23.236 units
D = 23.236 units/3.14 = 7.4 units
r = D/2 = 3.7 units
C = 23.376 units
D = 23.376 units / 3.14 = 7.4 units
r = D/2 = 3.7 units
C = 13.188 units
D = 13.188 units/3.14 = 4.2 units
r = D/2 = 2.1 units
